iPhone Possessed/Hacked -- Next steps?

I'm a from-the-beginning iPhone and long-time Mac user, so I'm familiar with operations and practice safe internet behavior, all my apps have been from the Apple Store, and my phone has never been jailbroken.

The last two mornings I've come downstairs and found that my iPhone 6 has been busy overnight while it was charging. The first morning, when I unlocked it, the mail app was on a different message than when I went to bed and numerous emails that came between 2 and 4 a.m. had been marked read.

This morning when I came down, music was playing from the iPhone, the lock screen indicated that touchID had been disable (either because of restart or failed entries), the rotation lock had been turned on, numerous email messages had been marked read, dozens of safari tabs were open, Google Maps had been searching for gas stations near Tacoma, Washington (I've never been there, but here it's nice), six random emails to contacts had been sent with gibberish text, two phone calls had been made to contacts (sure they appreciated that at 1:34 a.m.), and an Amazon Firestick had been ordered for delivery to my house.

I've got three theories: (1) somehow my phone has been hacked; (2) it's not interacting well with my anker charger (which has in the past not allowed me to type while the charger is plugged in and charging the phone) and the lightning cable is simply sending random strings to the phone; or (3) my phone is possessed.

Any suggestions for next steps to diagnose/prevent? This is a fully updated iPhone 6 from around launch day.